The speed requirements for decoders for Reed-Solomon codes and other cyclic BCH codes, which involve finding the roots of a polynomial over a finite field, continue to increase. One approach to increasing decoder speed may be to parallelize the polynomial search. However, it would be rare for the length of the codeword to be an integer multiple of the number of parallel processing streams; indeed, in most cases that would be expected not to be true. Therefore, the polynomial search normally would not be aligned with the data, requiring substantial additional logic to keep track of the data alignment.